Randomness

The term randomness is often used in statistics to signify well defined statistical properties, such as lack of bias or correlation. Random is different from arbitrary, because to say that a variable is random means that the variable follows a probability distribution. Arbitrary on the other hand implies that there is no such determinable probability distribution for the variable.

He who believes this (atomism) may as well believe that if a great quantity of the one-and-twenty letters, composed either of gold or any other matter, were thrown upon the ground, they would fall into such order as legibly to form the Annals of Ennius. I doubt whether fortune could make a single verse of them.

The theory says a lot, but does not really bring us any closer to the secret of the 'old one'. I, at any rate, am convinced that He does not throw dice.

Albert Einstein, letter to Max Born, 4 December 1926; commonly paraphrased "God does not play dice with the universe."

Events may appear to us to be random, but this could be attributed to human ignorance about the details of the processes involved.

Brain S. Everitt, Chance Rules (1999), Chapter 12, p. 175.

Perhaps randomness is not merely an adequate description for complex causes that we cannot specify. Perhaps the world really works this way, and many events are uncaused in any conventional sense of the word.

A random sequence is a vague notion in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests traditional with statisticians and depending somewhat on the uses to which the sequence is to be put.

Dick Lehmer (1951), cited by Julian Havil in The Irrationals: A Story of the Numbers You Can't Count On (2012), Chapter 9, p. 229.

Existence is random. Has no pattern save what we imagine after staring at it for too long. No meaning save what we choose to impose. This rudderless world is not shaped by vague metaphysical forces. It is not God who kills the children. Not fate that butchers them or destiny that feeds them to the dogs. It’s us. Only us.

One of us recalls producing a 'random' plot with only 11 planes, and being told by his computer center's programming consultant that he had misused the random number generator: 'We guarantee that each number is random individually, but we don’t guarantee that more than one of them is random.' Figure that out.

The definition of random in terms of a physical operation is notoriously without effect on the mathematical operations of statistical theory because so far as these mathematical operations are concerned random is purely and simply an undefined term.